166. If   a3 +	1	= 2 , then value of	a2 + 1	is (a is a positive number.)
     	a3		a

1. 1. 1

   
   
   

   2. 2

   
   
   

   3. 3

   
   
   

   4. 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   a3 +	1	= 2
   	a3

   
   ⇒  a⁶ + 1 = 2a³
   ⇒  a⁶ – 2a³ + 1 = 0
   ⇒  (a³ – 1)² = 0
   ⇒  a³ – 1 = 0
   ⇒  a³ = 1 ⇒ a = 1
   

   ∴	a2 + 1	= 1 + 1 = 2
   	a

   Correct Option: B

   a3 +	1	= 2
   	a3

   
   ⇒  a⁶ + 1 = 2a³
   ⇒  a⁶ – 2a³ + 1 = 0
   ⇒  (a³ – 1)² = 0
   ⇒  a³ – 1 = 0
   ⇒  a³ = 1 ⇒ a = 1
   

   ∴	a2 + 1	= 1 + 1 = 2
   	a

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167. If the vertices of a quadrilateral are A(– 2, 6), B(1, 2), C(10, 4) and D(7, 8). Then the equation of diagonal AC will be ?

1. 1. x + 6y = 34

   
   
   

   2. x – 6y = 34

   
   
   

   3. x + 2y = 1

   
   
   

   4. x – y = 13

   
   
   

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1. View Hint View Answer Discuss in Forum

   We know that, equation of line is
   

   y − y1	=	x − x1
   y2 − y1		x2 − x1

   
   
   12y – 72 = –2x – 4
   2x + 12y = –4 + 72
   2x + 12y = 68
   ⇒  x + 6y = 34

   Correct Option: A

   We know that, equation of line is
   

   y − y1	=	x − x1
   y2 − y1		x2 − x1

   
   
   12y – 72 = –2x – 4
   2x + 12y = –4 + 72
   2x + 12y = 68
   ⇒  x + 6y = 34

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168. Find the equation of the line which passes through the point (2, 2) and makes an angle of 45° with x-axis ?

1. 1. x + y = 2

   
   
   

   2. x – y = 0

   
   
   

   3. 2x + y = 3

   
   
   

   4. x – 2y = 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the equation of line be
   y – y₁ = m(x – x₁)
   As it passes through (2, 2) and having slope m = tan 45° = 1
   ⇒  y – 2 = 1(x – 2)
   y – x = 0
   or
   x – y = 0

   Correct Option: B

   Let the equation of line be
   y – y₁ = m(x – x₁)
   As it passes through (2, 2) and having slope m = tan 45° = 1
   ⇒  y – 2 = 1(x – 2)
   y – x = 0
   or
   x – y = 0

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169. The value of x, if the slope of the line joining (–8, 11), (2, x) is		−4		will be
     		3

1. 1. −7

      3

   
   
   

   2. 7

      3

   
   
   

   3. 1

      3

   
   
   

   4. 5

      3

   
   
   

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1. View Hint View Answer Discuss in Forum

   We know that
   

   Slope of a line =	y2 − y1
   	x2 − x1

   
   

   –4	=	x − 11
   3		2 + 8

   
   

   ⇒	–4	=	x − 11
   	3		10

   
   ⇒  –40 = 3x – 33
   ⇒  –40 + 33 = 3x
   ⇒  –7 = 3x
   

   ⇒  x =	–7
   	3

   Correct Option: A

   We know that
   

   Slope of a line =	y2 − y1
   	x2 − x1

   
   

   –4	=	x − 11
   3		2 + 8

   
   

   ⇒	–4	=	x − 11
   	3		10

   
   ⇒  –40 = 3x – 33
   ⇒  –40 + 33 = 3x
   ⇒  –7 = 3x
   

   ⇒  x =	–7
   	3

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170. ₹120 is divided between x, y and z, so that x’s share is ₹20 more than y’s and ₹20 less than z’s. What is y’s share?

1. 1. ₹25

   
   
   

   2. ₹20

   
   
   

   3. ₹30

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   x = Rs, (y + 20)
   z = Rs. (y + 40)
   ∴  y + y + 20 + y + 40 = 120
   ⇒  3y = 60
   ⇒  y = Rs. 20

   Correct Option: B

   x = Rs, (y + 20)
   z = Rs. (y + 40)
   ∴  y + y + 20 + y + 40 = 120
   ⇒  3y = 60
   ⇒  y = Rs. 20

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